461 research outputs found
Operator mixing in N=4 SYM: The Konishi anomaly revisited
In the context of the superconformal N=4 SYM theory the Konishi anomaly can
be viewed as the descendant of the Konishi multiplet in the 10 of
SU(4), carrying the anomalous dimension of the multiplet. Another descendant
with the same quantum numbers, but this time without anomalous
dimension, is obtained from the protected half-BPS operator (the
stress-tensor multiplet). Both and are renormalized mixtures
of the same two bare operators, one trilinear (coming from the superpotential),
the other bilinear (the so-called "quantum Konishi anomaly"). Only the operator
is allowed to appear in the right-hand side of the Konishi anomaly
equation, the protected one does not match the conformal properties of
the left-hand side. Thus, in a superconformal renormalization scheme the
separation into "classical" and "quantum" anomaly terms is not possible, and
the question whether the Konishi anomaly is one-loop exact is out of context.
The same treatment applies to the operators of the BMN family, for which no
analogy with the traditional axial anomaly exists. We illustrate our abstract
analysis of this mixing problem by an explicit calculation of the mixing matrix
at level g^4 ("two loops") in the supersymmetric dimensional reduction scheme.Comment: 28 pp LaTeX, 3 figure
Chiral rings, anomalies and loop equations in N=1* gauge theories
We examine the equivalence between the Konishi anomaly equations and the
matrix model loop equations in N=1* gauge theories, the mass deformation of N=4
supersymmetric Yang-Mills. We perform the superfunctional integral of two
adjoint chiral superfields to obtain an effective N=1 theory of the third
adjoint chiral superfield. By choosing an appropriate holomorphic variation,
the Konishi anomaly equations correctly reproduce the loop equations in the
corresponding three-matrix model. We write down the field theory loop equations
explicitly by using a noncommutative product of resolvents peculiar to N=1*
theories. The field theory resolvents are identified with those in the matrix
model in the same manner as for the generic N=1 gauge theories. We cover all
the classical gauge groups. In SO/Sp cases, both the one-loop holomorphic
potential and the Konishi anomaly term involve twisting of index loops to
change a one-loop oriented diagram to an unoriented diagram. The field theory
loop equations for these cases show certain inhomogeneous terms suggesting the
matrix model loop equations for the RP2 resolvent.Comment: 23 pages, 3 figures, latex2e, v4: minor changes in introduction and
conclusions, 4 references are added, version to appear in JHE
Effective Superpotentials via Konishi Anomaly
We use Ward identities derived from the generalized Konishi anomaly in order
to compute effective superpotentials for SU(N), SO(N) and
supersymmetric gauge theories coupled to matter in various representations. In
particular we focus on cubic and quartic tree level superpotentials. With this
technique higher order corrections to the perturbative part of the effective
superpotential can be easily evaluated.Comment: 17 pages, harvma
World-sheet Stability of (0,2) Linear Sigma Models
We argue that two-dimensional (0,2) gauged linear sigma models are not
destabilized by instanton generated world-sheet superpotentials. We construct
several examples where we show this to be true. The general proof is based on
the Konishi anomaly for (0,2) theories.Comment: 18 pages, LaTe
On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture
In this paper we study the nonperturbative corrections to the generalized
Konishi anomaly that come from the strong coupling dynamics of the gauge
theory. We consider U(N) gauge theory with adjoint and Sp(N) or SO(N) gauge
theory with symmetric or antisymmetric tensor. We study the algebra of chiral
rotations of the matter field and show that it does not receive nonperturbative
corrections. The algebra implies Wess-Zumino consistency conditions for the
generalized Konishi anomaly which are used to show that the anomaly does not
receive nonperturbative corrections for superpotentials of degree less than
2l+1 where 2l=3c(Adj)-c(R) is the one-loop beta function coefficient. The
superpotentials of higher degree can be nonperturbatively renormalized because
of the ambiguities in the UV completion of the gauge theory. We discuss the
implications for the Dijkgraaf-Vafa conjecture.Comment: 23 page
Konishi anomaly approach to gravitational F-terms
We study gravitational corrections to the effective superpotential in
theories with a single adjoint chiral multiplet, using the generalized Konishi
anomaly and the gravitationally deformed chiral ring. We show that the genus
one correction to the loop equation in the corresponding matrix model agrees
with the gravitational corrected anomaly equations in the gauge theory. An
important ingrediant in the proof is the lack of factorization of chiral gauge
invariant operators in presence of a supergravity background. We also find a
genus zero gravitational correction to the superpotential, which can be removed
by a field redefinition.Comment: 28 pages, uses JHEP3.cl
Gravitational F-terms of N=1 Supersymmetric SU(N) Gauge Theories
We use the generalized Konishi anomaly equations and R-symmetry anomaly to
compute the exact perturbative and non-perturbative gravitational F-terms of
four-dimensional N=1 supersymmetric gauge theories. We formulate the general
procedure for computation and consider chiral and non-chiral SU(N) gauge
theories.Comment: 25 pages, v2: minor changes in section 4, references adde
Konishi anomaly and N=1 effective superpotentials from matrix models
We discuss the restrictions imposed by the Konishi anomaly on the matrix
model approach to the calculation of the effective superpotentials in N=1 SUSY
gauge theories with different matter content. It is shown that they correspond
to the anomaly deformed Virasoro constraints .Comment: Latex, 8 pages, misprint and the normalization of the condensate in
the elliptic model are correcte
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